A transportation and dispenser box is known from the leaflet “Das CORNUFLEX Compact System”, edition 1/1995 of the Applicant. The leaflet shows a portion of cardboard, corrugated cardboard and the like in which a sheet material of material being wound up on a bobbin is placed in an upright box. The upper bottom wall or cover wall is designed as a flap with a closing tongue element, and after having inserted the roll, it may be moved to reach the closed position. An opening is located between the closing flap and the respective vertical side wall, the opening serving for the sheet material passing out off the box. The sheet material is wound up on a bobbin to form a roll, the width of the sheet material being identical to the length of the bobbin. The sheet material being wound up on the bobbin to form a roll is an elastic structure having a respective diameter and respective elastic properties depending on the winding conditions. The square cross-section of the portion of the transportation and dispenser box is chosen such that the roll in the closed position of the upright portion in the region of all bottom walls, side walls and front walls contacts the material of the portion. When the roll has been wound up in a rather loose way, it has sort of a surface contact to the bottom walls and the side walls. Consequently, when pulling the sheet material out off the box, a relatively great resistance has to be overcome. Furthermore, the square cross-section has been designed to be rather small to reduce the cost of the package material. When using the known box, there is the danger of an item already being torn apart at its perforation when the perforation is still located in the interior of the transportation and dispenser box. In such a case, the user may use the item, but the end of the sheet material is still located inside of the box such that there only is the possibility of opening the transportation and dispenser box to reach the end of the sheet material, and to then move the end out off the box. When using rolls including a comparatively great number of items along the sheet material and having a respective increased width, there is a respectively increased weight and respectively increased friction of the roll in the transportation and dispenser box when pulling the sheet material towards the outside. Frictional conditions are also often disadvantageous with respect to the frictional properties existing between the sheet material and the inner side of the transportation and dispenser box such that easy pulling is prevented. It is especially disadvantageous to handle sheet materials being wound up to form a roll in a comparatively soft manner. Consequently, the rolls are elastic, and there is a comparatively great surface of contact to the inner wall of the transportation and dispenser box. This is especially disadvantageous when tearing apart the first item from the sheet material, but it is also relevant when the diameter of the roll has already diminished due to having removed a number of items from the roll. Depending on the relative position of the opening for exiting the path of material from the box in an outward direction with respect to the tangential direction of the path of material on the roll, there may be additional frictional forces to be overcome in the region of the opening.